Expanded chains Subject

T want to finish this introduction by a short sketch of the history of the subject. The physics of dilute polymer solutions by now has been ail active field for about TO years. Much of the early work is connected to the name of Flory and summarized in his classic books [Flo53, Fit>69], Up to about. 1970 much theoretical or experimental work concentrated on the behavior in the dilute limit, where via virial expansions the problem can be reduced to considering only a few interacting chains. The development led to the so-called two parameter theories , which essentially expand quantities like Rg or A2 in powers of z, In 1971 these developments were most carefully reviewed in a book by Yamakawa [Yam.71]. 

One of the most important phenomena in the polymer solvation is the change in the overall size of the polymer chain upon solvation. In fact at equilibrium the average size of isolated polymer molecules in solution is a function of solvent quality and varies from expanded conformations in good solvents to random walk conformations in poor solvents. This is referred to as collapse transition and was first predicted by Stockmayer [82] more than 45 years ago. The phenomenon was observed by Nishio et al. [83] and Swislow et al. [84] more than 25 years ago and is still a subject of much experimental, computational, and theoretical research today. So far many investigators have tried to study the chain size with solvation using a variety of methods. 

During the past nine years the subject of total synthesis of sugars and cyclitols has been vividly developed. The discovery of a large number of unusual sugars in nature—deoxy, amino, branched chain sugars (many of them components of antibiotics)—made their synthesis attractive. On the other hand, improvements in organic reagents and synthetic methods allowed a return to older preparations which could be now better performed. Finally, some synthetic ideas already described in this series, in the first chapter of the volume on the total synthesis of carbohydrates, are further expanded. 

In other words, the local deformation energy is quadratic in the local curvature k s) when expanded to the lowest order in k. Conformations with Rlocal deformation energy greater than k T per unit length. Subjecting this model to thermal fluctuations results in the wormlike chain model. ... 

This approach has been expanded by Robertson (1979) who examined the relationship between molecular relaxation events that occur via small, simple trans, and gauche conformational changes in the chains and the free volume distribution. The former are assumed to be coupled with the fi ee volume environment which will also be subject to thermal fluctuations. 

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